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2022
- ISIDORE Id: 10670/1.4d5647...
- isbn: 978-3-031-07014-3
- hal: hal-03872875
- doi: 10.1007/978-3-031-07015-0_4
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info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-031-07015-0_4
info:eu-repo/semantics/OpenAccess
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Alexandre Popoff et al., « An Interactive Tool for Composing (with) Automorphisms in the Colored Cube Dance », HAL SHS (Sciences de l’Homme et de la Société), ID : 10.1007/978-3-031-07015-0_4
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The 'colored Cube Dance' is an extension of Douthett's and Steinbach's Cube Dance graph, related to a monoid of binary relations defined on the set of major, minor, and augmented triads. This contribution explores the automorphism group of this monoid action, as a way to transform chord progressions. We show that this automorphism group is of order 7776 and is isomorphic to (Z 3 4 D 8) (D 6 × Z 2). The size and complexity of this group makes it unwieldy: we therefore provide an interactive tool via a web interface based on common HTML/Javascript frameworks for students, musicians, and composers to explore these automorphisms, showing the potential of these technologies for math/music outreach activities.
